Section 3.3 Quadratic Functions. A quadratic function is a function of the form: where a, b, and c are real numbers and a 0. The domain of a quadratic.

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Presentation transcript:

Section 3.3 Quadratic Functions

A quadratic function is a function of the form: where a, b, and c are real numbers and a 0. The domain of a quadratic function consists of all real numbers. The graph of a quadratic function is called a parabola.

Graphs of a quadratic function f(x) = ax 2 + bx + c, a 0 a > 0 Opens up Vertex is lowest point Axis of symmetry a < 0 Opens down Vertex is highest point Axis of symmetry

Graph the function fxxx()  Find the vertex and axis of symmetry by Completing the square first.

(0,0) (2,4) (0,0) (2, -8) Now use the methods of Chapter 2 to Graph.

(2, 0) (4, -8) (2, 7) (4, -1) Vertex : (2,7)

Properties of the Quadratic Function Parabola opens up if a > 0. Parabola opens down if a < 0.

Given the function, determine whether the graph opens upward or downward. Find the vertex, axis of symmetry, the x- intercepts, and the y-intercept. fxxx()  x-coord. of vertex: y-coord. of vertex: Axis of symmetry: x b a    2 3 Vertex: (-3, -13)

fxxx()  y-intercepts: f(0) = 5; so the y-intercept is (0,5) x-intercepts: Solve the equation = 0 fxxx()  The x-intercepts are approximately (-5.6,0) and (-.45,0) Summary: Parabola opens up Vertex (-3, -13) y-intercept: (0,5) x-intercepts: (-0.45, 0) and (-5.55,0)

Now, graph the function using the information found in the previous steps. Vertex: (-3, -13) (-5.55, 0)(-0.45, 0) (0, 5)